Finite element methods: superconvergence, post-processing, and a posteriori estimates

Michel Krizek, Pekka Neittaanmaki, Rolf Stenberg0824701488, 9780824701482, 9780585367576

Based on the proceedings of the first conference on superconvergence held recently at the University of Jyväskylä, Finland, this unique resource presents reviewed papers focusing on superconvergence phenomena in the finite element method. Keeping abreast of this rapidly developing field of research, Finite Element Methods surveys for the first time all known superconvergence techniques, including their proofs considers superconvergence phenomena observed on meshes that are locally symmetric with respect to one point, quasiuniform, locally periodic, and self-similar discusses techniques and methods such as post-processing schemes examines a posteriori error estimates for finite element solutions of differential equations that yield reliable bounds for the error in the computed solution analyzes problems related to mathematical physics and much more Helpfully complemented with more than 2150 bibliographic citations, equations, and drawings, this excellent reference is required reading for numerical analysts, applied mathematicians, software developers, researchers in computational mathematics, and graduate-level students in these disciplines.